Question

Find the ratio in which the y-axis divides the line segment joining the points
A(-4, 2) and B(3, 9). Also find the coordinates of the point of division.
​

Answer 1

Step-by-step explanation:

Using the section formula, if a point (x,y) divides the line joining the points (x

1

,y

1

) and (x

2

,y

2

) in the ratio m:n, then

(x,y)=(

m+n

mx

2

+nx

1

,

m+n

my

2

+ny

1

)

Let y−axis divides the line joining points A(−4,−6) and B(10,12) in ratio y:1

Then, as per section formula the coordinates of point which divides the line is

y+1

10y−4 ,

y+1

12y−6

We know that coordinate at y−axis of point of x is zero

Then,

y+1

10y−4

=0

⇒10y−4=0

⇒10y=4

⇒y=

4

10

=

2

5

Then, ratio is

5

2

:1⇒2:5

Substitute the value of y in y− coordinates, we get

5

2

+1

12

5

2

−6

=

2−5

24−30

=

−3

−6

=2

Then, coordinates of point which divides the line joining A and B is (0,2) and ratio

5

2